Path
Planning for Formations using Global Optimization with Sparse Grids

M. Saska, I. Ferenczi, M. Hess, and K. Schilling
(Germany)

Keywords

mobile robot, formations, splines, global optimization,
sparse grids

Abstract

This paper proposes an original path planning method
developed for leader following formations of car-like
robots. In this approach a reference path calculated by the
leader should be feasible for all following robots without
changing a relative distance in the formation. This require
ment can be satisﬁed using a solution which is composed of
smoothly connected cubic splines and can be calculated in
real time. Qualities of the result like the length and minimal
radius of the resulting path as well as the distance to obsta
cles are merged into a discontinuous penalty function. The
resulting global minimization problem is solved with a de
terministic approach based on sparse grids. This algorithm
has been tested for several applications in real robotics en
vironments and compared with the results from a stochastic
Particle Swarm Optimization method. Some of the deter
mined solutions were then veriﬁed by simulations of for
mation movements.